1) Generally, 95% confidence indicates that the mean effect of the drug is larger than the mean effect of the placebo 95% of the time over many repetitions.

Assumptions are: what distribution is used to calculate confidence, the sample size, width of interval, is the control group independent of the drug group or is it a longitudinal study, is there any regression toward the mean, etc.

2) This question could be difficult or easy. I would answer this question assuming that the other players pick a number 1, 2, or 3 at random.

Assuming random picks, there are 27 combinations of (a, b, c) where a, b, c are the players and a, b, and c can take on 1, 2, or 3. If you list all combinations, you will win 8/27 times if you pick completely at random, but 4 of those wins will be if you pick the number 1. As, there are 9 combinations of picks when you choose 1, you win 4/9 of the time if you pick 1, 2/9 each player 2 and player 3 will win, and the company will win if you all pick 1.

Thus, I would pick 1. Of course, all players, if intelligent would know that 1 is the best, so there could be some psychological game theory considerations, but I don't think that is what the question is asking.

Hope this helps.

[This question took 10 minutes to answer]